Thank you all for the ideas.
Perhaps a little bit more information, I'm just thinking about a system so I'm not building it yet.
In the most simple form, let's assume I'm building a chess engine. In 'simple' AI, a search algorithm will look for an optimal solution (e.g. depth first search, alpha beta with cut off ...). in order to determine 'optimal' it might make use of a formula that calculates the 'value' of a given position. (e.g. the input is a FEN notation, the output an integer representing the value of the position).
This would require an AI to calculate the value of every possible position in the search tree.
I could just write a formula to do so and run the whole program on my PC. I think it is more interesting to build a distributed system that calculates these values before hand (let's say the most common positions) and does this using a cheap network of agents (i.e. arduino, ESP8266 ...).
Knowing myself, I'm sure that I will start with a really simple formula but will want to update it to ensure it plays strong against human players. Each update would of course need to recalculate all positions (well a subset determined by space on my HD).
Simple example, the very first calculation used is often just scoring all pieces (pawn = 1, knight = 2, bishop = 3). After a while you might notice that the value of a knight might be 2.5 of the value of a bishop = 3 if you have a pair but 2.5 if not ... This new formula now needs to be used by the agents (arduino).
david_2018: The idea of using an EEPROM seems like an elegant solution, I could potentially hook up all arduino's to the same EEPROM so I would need only one.
This sparks a new idea, I could build a PCB with a load of atmega chips, using SPI or something similar to communicate with a master (that gets all the positions and the formula from MQTT) and build a sort of parallel specialist computer. I just don't have the skills or knowledge yet to do so :-)
gfvalvo: The suggestion of parameterising the formula will work in the beginning until you decide that the value of a knight differs from the begin and middle / end game. Of course I could try to write all formulas beforehand and then select the correct one with a parameter but that would not allow me to add a new formula without uploading new sketches to all agents. It will however be good enough to start with.
Klaus_K, you are correct, I come from a PC/GUI programming background and the design patterns can not just be transferred to the microcontroller world. I will need to further inform myself on how microcontrollers are networked and how they communicate with each other (and generally how they work). Thank you for the information.